Make the tomato relish: in a medium bowl, combine the chopped, seeded tomatoes, 1 tablespoon extra-virgin olive oil, 2 tablespoons balsamic vinegar, and a pinch of kosher salt and black pepper; stir to combine and refrigerate if desired for up to 24 hours.
Prepare the chicken: place each chicken breast between plastic wrap on a cutting board and pound to about 1/8-inch thickness, then season both sides with kosher salt and black pepper.
Assemble: spread about 2 tablespoons of pesto over each pounded breast, then top evenly with shredded mozzarella.
Roll and secure: roll each breast tightly and secure with kitchen twine or toothpicks so the filling stays inside.
Sear: heat 2 tablespoons olive oil in a large skillet over medium-high heat and brown the rolls on all sides, about 10 to 15 minutes total.
Bake: lightly spray a shallow baking dish with cooking spray, place the seared chicken rolls seam-side down, and bake in a 400°F oven for about 15 minutes or until the internal temperature reaches 165°F.
Finish and serve: remove twine or toothpicks, slice each roll into 3–4 medallions, top with a spoonful of tomato relish, and serve immediately.